概称句词项逻辑的树图判定算法

概称句的形式刻画研究始于人工智能。从条件蕴涵引入开始,到建立概称句词项逻辑的形式系统GAG和Gaa,关于概称句这一系列的研究主要是围绕概称句自身性质的探讨,以试图对于概称句推理给出更合理的形式刻画,而没有同时兼顾计算机应用方面的考虑。回归问题的初始,关于概称句的概念理论是否还可以用于计算机科学领域,是这一研究路线所面临的问题。首先要解决的问题是,根据GAG和Gaa模型,公式的可满足性是否有能行的判定方法。对此本文给出了基于GAG语义的树图判定算法,包括相应的可靠性,完备性等证明。     

通过演绎方式得概称句推理的逻辑

基于[4]中的逻辑系统G,本文通过删减和增加公理及规则给出3个逻辑G0,GD和Gs,同时,我们通过对正常主项选择函数添加不同的条件给出与三个逻辑相应的不同的模型定义。其中,G0是GD和Gs的基础。这些逻辑的给出是为了刻画通过演绎方式得概称句的推理的局部推理。     

涵义语义与关于概称句推理的词项逻辑

概称句推理具有以词项为单位的特征并且词项的涵义在其中起到了重要的作用。已有的处理用A一表达式表达涵义,不够简洁和自然。亚里斯多德三段论是一种词项逻辑,但它是外延的和单调的。这两方面的情况使得有必要考虑新的词项逻辑。涵义语义的基本观点是：语词首先表达的是涵义,通过涵义的作用,语词有了指称,表达概念。概称句三段论是更为常用的推理,有两个基本形式GAG和Gaa。在涵义语义的基础上建立的系统GAG和Gaa是关于这两种推理的公理系统。     

概称句的语义解释及形式化比较研究

概称句的研究始于20世纪70年代,由于概称句在思维和语言中不可或缺的地位,语言学、逻辑学、人工智能、哲学、心理学等多个领域的研究者分别从不同角度对概称句进行研究,时至今日已经提出了多种理论和形式处理方法。尽管研究视角、方法不同,对概称句进行语义分析都是研究的必经之路。本文从逻辑学研究视角,以概称句的特点为依据,将部分概称句语义研究的成果做总结和梳理,力图抓住各研究方向的思想本质,并通过论证指出周北海及毛翊[1]比较透彻地分析了概称句语义,抓住了概称句的本质。一概称句特点概述概称句(genericsentences)大体上指不表示…     

概称句词项逻辑系统GAG与Gaa的完全性

GAG与Gaa是关于概称句推理的逻辑系统。概称句词项逻辑的要点是引入了表示概念的词项,从而以更自然的方式表示概念在推理中的作用,这也带来了概称句词项逻辑语言的特点。涵义语义是用于概称句词项逻辑语言的形式语义。在涵义语义下GAG与Gaa是可靠的,但是完全性证明一直空缺。通过完全性证明,发现有必要对原来的涵义语义做一些补充和完善,为此提出涵义语义结构的一般形式,进而给出全涵义结构和实涵义结构。原来的语义结构实际上是全涵义结构。完全性证明需要使用实涵义结构。实涵义结构的框架部分与解释函数有关,因而不完全独立于被解释的语言。实涵义结构更像是认知主义语义观下的语义构造。长期以来,实在论语义观在逻辑学研究中根深蒂固。实涵义结构的提出,对这类逻辑研究的哲学基础提出了反思。     

用概率方法解释概称句——亚里尔·科恩的概称句语义研究

用概率方法解释概称句,是概称句语义分析的一个方向。亚里尔·科恩(Ariel Cohen)[1]是近年来以概率视角对概称句进行分析研究的一位有代表性的学者,本文介绍亚里尔·科恩对概称句的解释,并以《概称句的语义解释及形式化比较研究》[2]一文中对概称句特点的讨论为依据,对科恩的解     

小学生数学推理能力结构的验证性因素分析

1　前言小学数学教学中 ,培养逻辑推理能力是培养学生数学能力的中心任务。而且 ,掌握比较完善的逻辑推理能力是儿童智力发展的重要环节和主要标志。国外心理学界对儿童推理的研究是很重视的。英国心理学家福勒 (Ｆｏｗｌｅｒ)曾通过 50 0名小学儿童以归纳、演绎、归纳和演绎结合三种推理进行实验教学。我国心理学界对小学儿童的推理特点也开展了一些研究 ,但对推理能力的结构成分划分大致仍为归纳、演绎、类比推理能力三种。小学数学教学大纲虽提出了推理能力的培养要求 ,但至于包括哪几方面的推理能力 ,并未进一步说明。鉴于此 ,本文欲对…     

传递性推理的认知与脑机制探讨

以抽象的内容作为实验材料,测定12名大学生在完成四种不同格式的传递性推理任务时的事件相关电位(ERP),探讨传递性推理过程的认知机制与脑内时程动态变化.结果发现,被试解决四种不同类型推理题目时的正确率和反应时差异均不显著;但是"谁最大"提问方式的正确率显著高于"谁最小"提问方式,另外,在任务类型①与④中"谁最大"提问方式的反应时显著短于"谁最小"提问方式.脑电数据结果表明,不同任务类型下,不同提问方式所诱发的ERP波形基本一致.空间表象模型与语言学模型都不能很好地解释以上结论,这似乎表明推理过程是很复杂的,人们往往会采用不同的信息加工策略来解决不同的推理问题,从而激活不同的大脑区域和神经通路.     

从现代逻辑观点看中国古代的有效推理

中国古代逻辑也是研究推理和论证的。推理和论证的主要目的是揭示一个命题为真的原因或理由。推理关系是一种 ＂必然地得出＂ 的关系。墨子提出了四种推理模式：＂辟＂、＂侔＂、＂援＂、＂推＂,而且把 ＂推＂ 又分为两种 ＂止＂,即归纳＂止＂ 式推论和演绎 ＂止＂ 式推论。特别地,墨家提出了 ＂效＂ 作为判定推理是否有效的标准。     

《因明正理门论》论式中的归纳成分

(1)陈那因明学说是在古因明学说归纳推理的基础上形成的。陈那对古因明的改革不彻底,从古因明学说中继承了一些归纳成分,这是陈那因明学说中归纳成分的来源。陈那学说中,三支的同喻依,因三相的第二相,九句因的第五句因都是归纳成分。(2)《因明正理门论》(以下简称《理门论》)推理理论的各部分都有归纳成分,使《理门论》的论式不是纯演绎推理,一个三支论式前提真,结论必然真,并且能举出同喻依,才满足“因明推理规则”。只有把《理门论》解释成根据“因明推理规则”进行推理,才符合《理门论》关于九句因、因三相和三支的论述。     

Generic statements require little evidence for acceptance but have powerful implications

Generic statements (e.g., "Birds lay eggs") express generalizations about categories. In this paper, we hypothesized that there is a paradoxical asymmetry at the core of generic meaning, such that these sentences have extremely strong implications but require little evidence to be judged true. Four experiments confirmed the hypothesized asymmetry: Participants interpreted novel generics such as "Lorches have purple feathers" as referring to nearly all lorches, but they judged the same novel generics to be true given a wide range of prevalence levels (e.g., even when only 10% or 30% of lorches had purple feathers). A second hypothesis, also confirmed by the results, was that novel generic sentences about dangerous or distinctive properties would be more acceptable than generic sentences that were similar but did not have these connotations. In addition to clarifying important aspects of generics' meaning, these findings are applicable to a range of real-world processes such as stereotyping and political discourse.     

Belief in reasoning

Reasoning has three types, deduction, induction, and abduction, of which we perceive deduction to be necessarily true, induction plausibly true, and abduction only hypothetically true. Syllogistic is a theory of deductive reasoning, introducing three figures of inferencing, of which figure-1 is obviously true, figure-3 and figure-2 are increasingly less transparent. We argue that the three figures of syllogistic and the three types of reasoning are related and their truth perceptions can be explained as different degrees of belief. We suggest that the source of this difference can be found in the conversion of a premise required by syllogistic processing. Experimental results illustrating our theory are included.     

Differential involvement of left prefrontal cortex in inductive and deductive reasoning

While inductive and deductive reasoning are considered distinct logical and psychological processes, little is known about their respective neural basis. To address this issue we scanned 16 subjects with fMRI, using an event-related design, while they engaged in inductive and deductive reasoning tasks. Both types of reasoning were characterized by activation of left lateral prefrontal and bilateral dorsal frontal, parietal, and occipital cortices. Neural responses unique to each type of reasoning determined from the Reasoning Type (deduction and induction) by Task (reasoning and baseline) interaction indicated greater involvement of left inferior frontal gyrus (BA 44) in deduction than induction, while left dorsolateral (BA 8/9) prefrontal gyrus showed greater activity during induction than deduction. This pattern suggests a dissociation within prefrontal cortex for deductive and inductive reasoning.     

Effects of directionality in deductive reasoning: II. Premise integration and conclusion evaluation

Previous research (Oberauer & Wilhelm, 2000) has shown an inherent directionality between the two terms linked in premises of typical deductive reasoning tasks. With three experiments we investigated the effect of inherent directionality on the time to integrate two premises and for the derivation of a conclusion. We varied figure (i.e., order of terms in the premises) and direction of inference (i.e., order of terms in the conclusion) in deduction tasks from various domains (propositional reasoning, syllogisms, spatial, temporal, and linear order reasoning). Effects of figure on premise reading times varied with the directionality of the relations. Effects of direction of inference reflected the same directionality for a subset of relations. We propose that two factors are jointly responsible for a large part of observed directionality effects in premise integration: the inherent directionality of relational statements and a general advantage for a given-new order of terms in the second premise. Difficulty of deriving a conclusion is affected by the directionality or relations if and only if the relation is semantically asymmetric, so that the directionality must be preserved in the integrated mental model.     

Expressing generic concepts with and without a language model

Utterances expressing generic kinds ("birds fly") highlight qualities of a category that are stable and enduring, and thus provide insight into conceptual organization. To explore the role that linguistic input plays in children's production of generic nouns, we observed American and Chinese deaf children whose hearing losses prevented them from learning speech and whose hearing parents had not exposed them to sign. These children develop gesture systems that have language-like structure at many different levels. The specific question we addressed in this study was whether the gesture systems, developed without input from a conventional language model, would contain generics. We found that the deaf children used generics in the gestures they invented, and did so at about the same rate as hearing children growing up in the same cultures and learning English or Mandarin. Moreover, the deaf children produced more generics for animals than for artifacts, a bias found previously in adult English- and Mandarin-speakers and also found in both groups of hearing children in our current study. This bias has been hypothesized to reflect the different conceptual organizations underlying animal and artifact categories. Our results suggest that not only is a language model not necessary for young children to produce generic utterances, but the bias to produce more generics for animals than artifacts also does not require linguistic input to develop.     

Is Skepticism about Self-Knowledge Coherent?

In previous work I argued that skepticism about the compatibility ofanti-individualism with self-knowledge is incoherent. Anthony Brueckner isnot convinced by my argument, for reasons he has recently explained inprint. One premise in Brueckner's reasoning is that a person'sself-knowledge is confined to what she can derive solely from herfirst-person experiences of using her sentences. I argue that Brueckner'sacceptance of this premise undermines another part of his reasoning – hisattempt to justify his claims about what thoughts our sincere utterances ofcertain sentences would express in various possible worlds. I describe aweird possible world in which a person who uses Brueckner's reasoning endsup with false beliefs about what thoughts her sincere utterances of certainsentences would express in various possible worlds. I recommend that wereject Brueckner's problematic conception of self-knowledge, and adopt onethat better fits the way we actually ascribe self-knowledge.     

Information learned from generic language becomes central to children’s biological concepts: Evidence from their open-ended explanations

Generic sentences (e.g., “Snakes have holes in their teeth”) convey that a property (e.g., having holes in one’s teeth) is true of a category (e.g., snakes). We test the hypothesis that, in addition to this basic aspect of their meaning, generic sentences also imply that the information they express is more conceptually central than the information conveyed in similar non-generic sentences (e.g., “This snake has holes in his teeth”). To test this hypothesis, we elicited 4- and 5-year-old children’s open-ended explanations for generic and non-generic versions of the same novel properties. Based on arguments in the categorization literature, we assumed that, relative to more peripheral properties, properties that are understood as conceptually central would be explained more often as causes and less often as effects of other features, behaviors, or processes. Two experiments confirmed the prediction that preschool-age children construe novel information learned from generics as more conceptually central than the same information learned from non-generics. Additionally, Experiment 2 suggested that the conceptual status of novel properties learned from generic sentences becomes similar to that of familiar properties that are already at the category core. These findings illustrate the power of generic language to shape children’s concepts.